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Compact finite difference schemes for the backward fractional Feynman–Kac equation with fractional substantial derivative

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Chinese Physics B 2019年第10期28卷 226-236页

作者：胡嘉卉王俊刚聂玉峰罗艳伟 Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an 710129China College of Science Henan University of TechnologyZhengzhou 450001China

The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the nonlocal time-space coupled fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the newly proposed approximation operators for fractional substantial derivative, we establish compact finite difference schemes for the backward fractional Feynman-Kac equation. The proposed difference schemes have the q-th(q = 1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. The numerical stability and convergence in the maximum norm are proved for the first order time discretization scheme by the discrete energy method, where an inner product in complex space is introduced. Finally, extensive numerical experiments are carried out to verify the availability and superiority of the algorithms. Also, simulations of the backward fractional Feynman-Kac equation with Dirac delta function as the initial condition are performed to further confirm the effectiveness of the proposed methods.

关键词： backward fractional Feynman-Kac equation fractional substantial derivative compact finite difference scheme numerical inversion of Laplace transforms

Law Professor: Changes "substantial" in China's Human Rights Conditions

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The Journal of Human Rights 2005年第3期4卷 10-10页

作者： STAFF REPORTER

"substantial" changes have taken place in China’s human rights conditions, according to Professor Xu Xianming, president of the China University of Law and Political Sciences. As a member of the Law Committee of the Standing Committee of the National People’s Congress, China’s highest legislature, he is known for his contributions to improvements in the country’s legal system. In an interview with Human Rights magazine, Professor Xu Xianming listed what he chose to call the "five most important changes" in China’s human rights conditions:

关键词： in China’s Human Rights Conditions Changes Law Professor substantial

A proof of Sethares' conjecture

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Science China Mathematics 2004年第2期47卷 236-244页

作者： YAO Guowu School of Mathematical Sciences Peking University Beijing 100871 China

Let ψ(z) be holomorphic in the unit disk △ and meromorphic on -△. Suppose f is a Teichmuller mapping with complex dilatation k-ψ/|ψ|. In 1968, Sethares conjectured that f is extremal if and only if either (i) ψ has a double pole or (ii) ψ has no pole of order exceeding two on △. The "if" part of the conjecture had been solved by himself. We will give the affirmative answer to the "only if" part of the conjecture. In addition, a more general criterion for extremality of quasiconformal mappings is constructed in this paper,which generalizes the "if" part of Sethares' conjecture and improves the result by Reich and Shapiro in 1990.

关键词： Teichmiiller mapping, extremality, Hamilton sequence, substantial boundary point.

Study on the Formation and Development of Xiaoyanwan Tiankeng in Xingwen World Geopark,Sichuan

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四川地质学报 2009年第S1期29卷 165-171页

作者： SHU Cheng-qiang1,ZHANG Bin1,SHUI Wei2,JIANG Liang-qun1,LIU Lijun1,QIN Fa-chao1(1.Land and Resources College,China West Normal University,Nanchong 637002,China 2.Agricultural college,Sichuan Agricultural University,Ya’ an 625014,China)

Chinese scholars Zhu xuewen put forward Tiankeng and defined it as a collapse feature which was diffe rent from the ordinary doline and developed in large-scale underground river *** paper analyzed the sasic conditions of Xiaoyanwan Tiankeng formation,such as sedimentary environment,climatic and hydrological conditions and so on;and deeply discussed the development course of Xiaoyanwan Tiankeng on this *** research result showed that Xiaoyanwan Tiankeng was completely accord with Tiankeng' definition,and was a well-developed and especially big Tiankeng in the maturation stages.

关键词： Xiaoyanwan Tiankeng substantial cave river Formation Karst

Do GMOs Accumulate Formaldehyde and Disrupt Molecular Systems Equilibria? Systems Biology May Provide Answers

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Agricultural Sciences 2015年第7期6卷 630-662页

作者： V. A. Shiva Ayyadurai Prabhakar Deonikar Systems Biology Group International Center for Integrative Systems Cambridge MA USA

Safety assessment of genetically modified organisms (GMOs) is a contentious topic. Proponents of GMOs assert that GMOs are safe since the FDA’s policy of substantial equivalence considers GMOs “equivalent” to their non-GMO counterparts, and argue that genetic modification (GM) is simply an extension of a “natural” process of plant breeding, a form of “genetic modification”, though done over longer time scales. Anti-GMO activists counter that GMOs are unsafe since substantial equivalence is unscientific and outdated since it originates in the 1970s to assess safety of medical devices, which are not comparable to the complexity of biological systems, and contend that targeted GM is not plant breeding. The heart of the debate appears to be on the methodology used to determine criteria for substantial equivalence. Systems biology, which aims to understand complexity of the whole organism, as a system, rather than just studying its parts in a reductionist manner, may provide a framework to determine appropriate criteria, as it recognizes that GM, small or large, may affect emergent properties of the whole system. Herein, a promising computational systems biology method couples known perturbations on five biomolecules caused by the CP4 EPSPS GM of Glycine max L. (soybean), with an integrative model of C1 metabolism and oxidative stress (two molecular systems critical to plant function). The results predict significant accumulation of formaldehyde and concomitant depletion of glutathione in the GMO, suggesting how a “small” and single GM creates “large” and systemic perturbations to molecular systems equilibria. Regulatory agencies, currently reviewing rules for GMO safety, may wish to adopt a systems biology approach using a combination of in silico, computational methods used herein, and subsequent targeted experimental in vitro and in vivo designs, to develop a systems understanding of “equivalence” using biomarkers, such as formaldehyde and glutathione, which predict m

关键词： substantial Equivalence Genetic Modification GMOs Formaldehyde Glutathione CytoSolve Systematic Review Systems Biology Bioinformatics Molecular Pathways C1 Metabolism Oxidative Stress Maize Methionine Biosynthesis Methylation Cycle Formaldehyde Detoxification

Wacker Greater China Saw 4% Growth in Sales for 2009

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China Chemical Reporter 2010年第7期21卷 8-8页

作者： Lily Wang

Wacker Chemie AG Greater China gained a 4% annual growth in sales for 2009 despite substantially lower semiconductor sales. Sales in China, including Taiwan province, which accounted for almost 60% of the Asiansales, increased to more than Euro 700 millionby rough calculation. Sales in the Asia-Pacific region accounted for 34% of the total sales, being Euro 1.25 billion. And the Munich-based chemical group reported sales of Euro 3.7 billion for 2009, down 13% year-on-year from Euro 4.3 billion for 2008. The downtrend was mainly due to a fall-off in orders from the semiconductor and construction industries.

关键词： Wacker accounted despite gained Taiwan substantial

GOTI Makes Off-Target Nowhere to Hide

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Bulletin of the Chinese Academy of Sciences 2019年第1期33卷 58-59页

作者： SINH SINH

On March 1st. a paper entitled“Cytosine base editor generates substantial off-target single nucleotide variants in mouse embryos”was published in Science, reporting a breakthrough technique accomplished by the CAS Institute of Neuroscience(ION), the CAS- MPC Partner Institute for Computational Biology(PICB) of the Shanghai Institute of Nutrition and Health of CAS, the Department of Genetics of Stanford University and the Agricultural Genome Institute at Shenzhen(AGIS) of Chinese Academy of Agricultural Sciences.

关键词： March substantial Sciences

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